The Mandelbrot set and the fractal nature of light, the Universe, and everything

Abstract

ABSTRACT"There is always another way to say the same thing that doesn't look at all like the way it was said before." Richard Feynman. In this essay, a novel approach to cosmology is presented that mathematically models the Universe as an iterated function system (IFS) analogous to the famous Mandelbrot Set IFS (M): z=z 2 +c, where z and c are complex numbers. In theoretical physics, wavefunctions are functions of a complex space that are commonly used to model the dynamics of particles and waves. In the IFS framework presented herein, complex dynamical systems are generated via the iteration process, where the act of iteration corresponds to 1) a change in the state of the system and 2) a change to the wavefunction itself. In this manner, M can be considered a wavefunction generator. In this framework, all observables, including gravity and time, are thought to be generated by the iteration process. Feynman understood that there are many ways of looking at the Universe that are equivalent in nature but different psychologically. Understanding cosmology in terms of fractals and iterated function systems requires a paradigm shift in the way we approach cosmology. This is an evidence based dissertation and does not contradict the standard model; rather, it attempts to reconstruct it using the principles of the fractal paradigm as outlined in this essay. It is the contention of the author that in order to understand the true nature of light, the universe and everything, we must first understand the important role that fractal cosmology plays in the study of our complex dynamical universe.Keywords: fractal, iteration, Mandelbrot set, wavefunction, black hole, event horizon, white hole, time, gravity, photon. PRELUDEThis essay presents a scientific framework; that can be applied to the whole of the universe; that avoids some of the historical paradoxes; that answers some of the previously unanswered questions; and offers a new understanding of the nature of light, the universe and everything. This approach to cosmology has philosophical implications which are addressed throughout this essay.

Spatial Statistics of Apollonian Gaskets

“…For instance, Figure 10 is the famous Grand Spiral Galaxy (NGC 1232), which can be simulated by a Mandelbrot set constructed from complex dynamics (see Figure 11). Both pictures are from [10]. Figure 10.…”

A tessellated continuum approach for the static analysis of perforated structures

“…which is, in fact, identical to Equation (2), where again the indexing associated with submaps is purposely absent here. The direct formulation is ideally suited to numerical work as the linear maps between triangular elements are readily handled numerically.…”

“…These geometries are known as fractal. Although interest in fractals has increased following Mandelbrot's work [2] their application to physical systems remains at best problematic. Practical application of fractals remains somewhat limited and references [3][4][5][6][7][8][9] provide a snapshot of what is evidently far from mainstream use.…”